Prologue: Why Math? A Historical Overview 

1  

The Nature of Problem Solving 


1  (50) 


3  (15) 

Inductive and Deductive Reasoning 


18  (10) 

Scientific Notation and Estimation 


28  (23) 


46  (5) 


51  (36) 

Sets, Subsets, and Venn Diagrams 


53  (8) 


61  (6) 


67  (10) 


77  (10) 


84  (3) 


87  (54) 


89  (8) 

Truth Tables and the Conditional 


97  (9) 

Operators and Laws of Logic 


106  (6) 


112  (10) 

Problem Solving Using Logic 


122  (9) 


131  (10) 


136  (5) 

The Nature of Numeration Systems 


141  (40) 


143  (8) 

HinduArabic Numeration System 


151  (4) 

Different Numeration Systems 


155  (6) 


161  (5) 

History of Calculating Devices 


166  (15) 


177  (4) 


181  (80) 


183  (8) 


191  (14) 


205  (8) 


213  (8) 


221  (9) 

Groups, Fields, and Real Numbers 


230  (12) 


242  (9) 


251  (10) 


256  (5) 


261  (82) 


263  (8) 


271  (5) 

Evaluation, Applications, and Spreadsheets 


276  (11) 


287  (8) 


293  (2) 


295  (5) 

Algebra in Problem Solving 


300  (12) 

Ratios, Proportions, and Problem Solving 


312  (9) 


321  (10) 

Modeling Uncategorized Problems 


331  (12) 


340  (3) 


343  (62) 


345  (10) 


355  (9) 


364  (7) 


371  (8) 

RightTriangle Trigonometry 


379  (8) 

Mathematics, Art, and NonEuclidean Geometries 


387  (18) 


401  (4) 

The Nature of Networks and Graph Theory 


405  (42) 

Euler Circuits and Hamiltonian Cycles 


407  (14) 

Trees and Minimum Spanning Trees 


421  (12) 


433  (14) 

Guest Essay: What Good Are Fractals? 


438  (4) 


442  (5) 

The Nature of Measurement 


447  (48) 


449  (9) 


458  (10) 

Surface Area, Volume, and Capacity 


468  (12) 

Miscellaneous Measurements 


480  (11) 


491  (4) 


492  (3) 


495  (32) 


497  (9) 


506  (8) 

Applications of Growth and Decay 


514  (13) 


524  (3) 

The Nature of Financial Management 


527  (74) 


529  (15) 


544  (9) 


553  (13) 


566  (11) 


577  (7) 


584  (8) 

Summary of Financial Formulas 


592  (9) 


596  (5) 


601  (36) 


603  (8) 


611  (8) 

Counting Without Counting 


619  (9) 

Rubik's Cube and Instant Insanity 


628  (9) 


633  (4) 

The Nature of Probability 


637  (56) 

Introduction to Probability 


639  (12) 


651  (9) 


660  (10) 


670  (13) 

Guest Essay: Extrasensory Perception 


680  (3) 

The Binomial Distribution 


683  (10) 


689  (4) 


693  (60) 

Frequency Distributions and Graphs 


695  (14) 


709  (12) 


721  (11) 

Correlation and Regression 


732  (8) 


740  (13) 


746  (7) 

The Nature of Graphs and Functions 


753  (46) 

Cartesian Coordinates and Graphing Lines 


755  (10) 


765  (2) 


767  (7) 


774  (13) 


787  (12) 


795  (4) 

The Nature of Mathematical Systems 


799  (58) 

Systems of Linear Equations 


801  (5) 

Problem Solving with Systems 


806  (11) 

Matrix Solution of a System of Equations 


817  (11) 


828  (15) 

Modeling with Linear Programming 


843  (14) 


853  (4) 

The Nature of Voting and Apportionment 


857  (60) 


859  (11) 


870  (18) 


888  (18) 


906  (11) 


914  (3) 


917  (2) 


919  (10) 


929  (6) 


935  (11) 


946  (7) 


953  
Epilogue: Why Not Math? Mathematics in the Natural Sciences, Social Sciences, and Humanities 

1  (1) 
Appendix A Glossary 

1  (1) 
Appendix B Selected Answers 

1  (1) 
Index 

1  